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12 August, 18:37

A cube has a volume of 10 cm^3. A larger cube has a volume of x cm^3. Consider the function f (x) = (x-10) cubed. What do the values f (19) and f (14) represent?

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  1. 12 August, 20:57
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    Hence both F (19) and F (14) has value for their indices.

    Step-by-step explanation:

    Given:

    A cube with volume = 10cm^3

    And a function=F (x) = (x-10) ^3.

    To find;

    Relationship between values at x=19 and x=14.

    Solution:

    Given that volume of cube = 10 c. c.

    So (l) ^3=10 c. c

    l = (10) ^ (1/3)

    l=2.15544 cm

    Now

    F (x) = (x-10) ^3

    here x=19

    F (19) = (19-10) ^3

    = (9) ^3

    =729 cc

    Now for x=14

    F (14)

    = (14-10) ^3

    = (4) ^3

    =64 cc

    Now concluding from above equation we get,

    The values are 729 and 64

    These two can be written in same value of index as follows:

    (729) = (9) ^3

    ={ (3) ^2}^3}.

    = (3) ^6

    And

    (64) = (4) ^3

    ={ (2) ^2}^3

    = (2) ^6.

    Hence both F (19) and F (14) has value for their indices.
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